An electron beam emitter typically includes an electron gun or generator, positioned within a vacuum chamber for generating electrons. The generated electrons can exit the vacuum chamber in an electron beam through an electron beam transmission or exit window that is mounted to the vacuum chamber. The exit window commonly has a thin metallic exit window foil, which is supported by a metallic support plate or grid. The support plate has a series of holes which allow electrons to reach and pass through the exit window foil. The support plate dissipates heat from the exit window foil caused by electrons passing through the exit window foil. However, electrons that are instead intercepted by the support plate areas between the holes cause heating of the support plate, which can reduce the ability of the support plate to dissipate heat from the exit window foil.